the difference in brass rod and steel is same as 12cm in all temperature.find the length of rod at 0c
Answers
Answer:
L1=l1(1+α1t)L1,L2= Final lengths
L2=l2(1+α2t)
L1−L2=l1−l2+t(l1α1−l2α2)
For difference to remain same
α1l1−α2l2=0⇒α1l1=α2l2.
Explanation:
Let Ls and Lb be the lengths at 0 degrees centigrade of the steel and brass rod respectively.
At some arbitrary temperatures x and y degrees centigrade, their lengths are given by
Lsx = Ls(1 + 12x*10^-6)] and Lbx = Lb(1 + 18x*10^-6]
Lbx - Lsx = Lb(1 + 18x*10^-6) - Ls(1 + 12x*10^-6) = 10 . . . . . . (1)and
Lby - Lsy = Lb(1 + 18y*10^-6) - Ls(1 + 12y*10^-6) = 10 . . . . . . (2)
(2) - (1) => Lb*(y - x)18*10^-6 - Ls*(y - x)12*10^-6 = 0
=> Ls/Lb = 3/2 . . . . . (3)
(3) and (1) => Lb[(1 + 18x*10^-6) - (3/2)Lb(1 + 12x*10^-6)] = 10 . . . . . . (4)
(4) => Lb = 10/[(1 + 18x*10^-6) - (3/2)(1 + 12x*10^-6)] for all x . . . . . (5)
(5) is an impossibility.
=> The difference in rod lengths can not remain at 10 cm at all temperatures.
=> The problem statement is erroneous.
the difference in brass rod and steel is same as 12cm in all temperature. find the length of rod at 0c
https://brainly.in/question/7141815
The difference in a brass rod and steel rod is same as 12cm at all temperature .Find the length of the rod at 0°C.(Alpha b =18×10^-6k^-1 and alpha s =12×10^-6k^-1)
https://brainly.com/question/19038373
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